CALCULATION OF THE PRESSURE TENSOR IN A FULLY IONIZED PLASMA

1963 ◽  
Vol 41 (11) ◽  
pp. 1787-1800 ◽  
Author(s):  
I. P. Shkarofsky
Keyword(s):  
Magnetic Fields ◽  
Flow Velocity ◽  
Planck Equation ◽  
Pressure Tensor ◽  
Laguerre Expansion ◽  
Fokker Planck Equation ◽  
Direction Cosines ◽  
Tensor Part ◽  
Fokker Planck

The tensor part of the pressure arising from gradients in flow velocity is calculated from the Fokker–Planck equation by using the Cartesian tensor expansion in direction cosines of the intrinsic velocity vectors and the Laguerre expansion for the magnitude of the intrinsic velocities. Wavelike perturbations and magnetic fields are included and both the electron and ion pressure tensors are investigated. The results are compared with those derived by other approaches.

CARTESIAN TENSOR EXPANSION OF THE FOKKER–PLANCK EQUATION

1963 ◽  
Vol 41 (11) ◽  
pp. 1753-1775 ◽  
Author(s):  
I. P. Shkarofsky
Keyword(s):  
Relaxation Times ◽  
Low Frequency ◽  
Planck Equation ◽  
Ion Distribution ◽  
Arbitrary Mass ◽  
Fokker Planck Equation ◽  
Energy Equipartition ◽  
Tensor Part ◽  
Ion Collision ◽  
Fokker Planck

The Fokker–Planck equation is expanded via Cartesian tensors. The results, valid for arbitrary mass ratio, reduce to known expressions for the f0, (isotropic) and f1 (directional) parts of the distribution. The same analysis also gives the relation for the f2 (tensor) part of the distribution. Nonlinear and recoil terms are also investigated. The f0 relation yields relaxation times and energy equipartition times for arbitrary velocity distributions. The ion recoil term is important for low-frequency waves in the electron f1 equation but is negligible in the electron f2 equation. The electron–electron contributions to the f1 and f2 collisional terms are of the same order as the electron–ion contributions. Except for momentum transfer calculations, the ion–ion collisional terms dominate over the ion–electron terms in the ion collision equations referring to the directional (F1) and tensor (F2) parts of the ion distribution.

AN APPLICATION OF FOKKER–PLANCK EQUATION TO JOSEPHSON JUNCTION

1989 ◽  
Vol 9 (1) ◽  
pp. 109-120
Author(s):  
G. Liao ◽  
A.F. Lawrence ◽  
A.T. Abawi
Keyword(s):  
Josephson Junction ◽  
Planck Equation ◽  
Fokker Planck Equation ◽  
Fokker Planck

scholarly journals Time-changed fractional Ornstein-Uhlenbeck process

2020 ◽  
Vol 23 (2) ◽  
pp. 450-483 ◽  
Author(s):  
Giacomo Ascione ◽  
Yuliya Mishura ◽  
Enrica Pirozzi
Keyword(s):  
Planck Equation ◽  
Uhlenbeck Process ◽  
Fokker Planck Equation ◽  
Ornstein Uhlenbeck Process ◽  
Fokker Planck

AbstractWe define a time-changed fractional Ornstein-Uhlenbeck process by composing a fractional Ornstein-Uhlenbeck process with the inverse of a subordinator. Properties of the moments of such process are investigated and the existence of the density is shown. We also provide a generalized Fokker-Planck equation for the density of the process.

Milne problem for a hard-sphere Rayleigh gas: A study based on the Fokker-Planck equation

1983 ◽  
Vol 28 (3) ◽  
pp. 1659-1661 ◽  
Author(s):  
S. Waldenstrøm ◽  
K. J. Mork ◽  
K. Razi Naqvi
Keyword(s):  
Hard Sphere ◽  
Planck Equation ◽  
Milne Problem ◽  
Fokker Planck Equation ◽  
Rayleigh Gas ◽  
Fokker Planck
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